You most likely need to update your Java and Flash plugins for Firefox and/or IE. Also, make sure that in your browser options, java and flash content are enabled. Also, once all that is updated, be sure to clear your cache just to be sure any pages are reloaded fresh.

Your next best move then is to try doing a speed test to see what your connection speed is. Speedtest.net has one (although there are hundreds of other ones too.) If it's just too low it might not even be able to load the plugins on YouTube (hence the errors.) If that's the case, you may have to check your connections and permissions and see if you are doing any sort of bandwidth limiting on your systems and if not, talk to your ISP.

Will, were you able to fix the youtube issue? We're experiencing the same issue at my work. It just started yesterday. Some videos play fine while others get the error and sometimes you can hit F5 to refresh it to play while other times it won't play at all. Any help would be appreciated. Thanks.